Newton's laws of motion form the cornerstone of classical mechanics and are pivotal in understanding linear motion. This section explores their application in scenarios involving linear motion of a particle with constant mass, particularly under various force conditions like friction, tension, and air resistance.

Newton's First Law of Motion

• Law of Inertia: A body at rest stays at rest, and a body in motion stays in motion unless acted upon by an external force.
• Problem: A soccer ball is lying still on a field. What keeps it at rest?
• Solution: Inertia. No external force is acting on it to change its state.

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Newton's Second Law of Motion

• Force Equation: Force equals mass times acceleration $F = ma$.
• Problem: Calculate the force needed to accelerate a $2 kg$ object at $3 m/s²$.
• Solution:$F = 2 kg × 3 m/s² = 6 N$.

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Newton's Third Law of Motion

• Action-Reaction: Every action has an equal and opposite reaction.
• Problem: If you push a wall with a force of $10 N$, what is the force exerted by the wall on you?
• Solution: $10 N$ in the opposite direction.

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Friction

• Friction: The resistive force between two surfaces.
• Problem: Calculate the frictional force for a $4 kg$ box on a surface with a friction coefficient of $0.5$.
• Solution: Frictional force = $0.5 × 4 kg × 9.81 m/s² = 19.62 N$.

Tension

• Tension: The force in a rope or string when stretched.
• Problem: Find the tension in a rope holding a $5 kg$ object at rest.
• Solution: Tension = $5 kg × 9.81 m/s² = 49.05 N$.

Air Resistance

• Air Resistance: The force opposing an object's motion through air.
• Problem: Estimate the air resistance on a falling object if the drag force is $10 N$.
• Solution: Air resistance = $10 N$.